Optical solitons in $\mathcal{PT}$-symmetric nonlinear couplers with gain and loss

TL;DR

This paper investigates the existence and stability of spatial and temporal solitons in $ ext{PT}$-symmetric nonlinear couplers with gain and loss, revealing how stability depends on a key parameter combination and describing the dynamics of unstable solitons.

Contribution

It provides a detailed analysis of soliton stability in $ ext{PT}$-symmetric couplers, identifying the key factors that determine stability and describing the behavior of unstable solitons.

Findings

Stability of solitons depends on a single combination of amplitude and gain/loss coefficient.

Unstable high-frequency solitons can lead to blowup or breather states.

Unstable low-frequency solitons can cause component separation and eventual blowup or breathing.

Abstract

We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.